### What is Young’s modulus?

**Young’s modulus, also known as the tensile modulus, elastic modulus or traction modulus** (measured in Pa, which is a pressure unit(N.m^-2; 10MPa is equivalent to 1Kg force per square millimeter) is a mechanical property of linear elastic materials. It, evaluates the elasticity of rigid or solid materials, which is the relation between the deformation of a material and the power needed to deform it. For example, a stiff material needs more force to deform compared to a soft material. Rubber has a 1MPa modulus, and iron has a 200GPa modulus (200.000 times more). For the same force applied to a sample with the same thickness, the rubber samples will extend 200.000 times more.

The deformation of a physical object depends first of all on the design geometry. Indeed, it’s easy to understand that a thick piece is harder to deform than a thin one.

The relation between force and deformation is the following :

Where:

-Epsilon is the elongation (Length / original Length) no unit

–Sigma is the stress in PA or PSI

– F is the force in N or lbf

– s is the transverse section in m² or in²

Applying a 400Kilo-force (4000N) to a 2cm radius (0.00126 section) 2 meter long steel rod with a Young’s modulus of 200 GPa, the rod will deform off 4000/(0.00126* 200.000.000)=0.016 and the rod will now measure 2.032m

### What is tensile strength?

Tensile strength is the value of the maximum stress that a material can handle. This is the limit between plasticity zone and rupture zone.

It’s important to notice the difference between resistance and elasticity.

A rubber band is easier to deform that a spaghetti but it’s harder to break.

### What is elongation at break ?

Elongation at break is the elongation that a material can withstand before breaking.It has no unit.

A rod of 10 cm at rest that is 15 before at break has an elongation at break of 0.5 sometimes written 50%.

### Stress-strain curve

There are mainly 3 types of behavior for a material, depending (among other variables) on the strength you use to deform it. Each of these behaviors are separated by yield points on the engineering stress-strain curve:

- Before the first yield point, the material will have an
**elastic behavior**, which means that it will go back to its initial state if we release the applied strength. - Beyond the elastic limit, the material will have a
**plastic behavior**, and permanent deformation will occur. For example, modeling clay always has a plastic behavior. - Finally, if the strength applied is too big, then the material will reach the
**ultimate strength point rupture point**. After this,the This is where it will break, but as it is linked to a lot of variables, such as the geometry of the object, it is difficult to know exactly when it will occur.